Download Geometry Homework Worksheets: Chapter 2

Geometry Homework Worksheets: Chapter 2
HW Set #1: Problems #1 - 8
For #1-4, choose the best answer for each multiple choice question.
1. Which of the following statements is/are
always true?
I. adjacent angles are acute
II. if m2  70 , then 2 is acute
III. two acute angles make a right angle
2. Identify the converse of the conditional statement
below:
A.
B.
C.
D.
E.
A.
B.
C.
D.
E.
I only
II only
III only
both I and II
I, II, and III
3. Identify a counterexample to the given
statement:
If  A is obtuse, then mA  120
A.
B.
C.
D.
E.
 A is an acute angle
 A is a right angle
mA  120
mA  80
mA  110
If I break my iPod, I will get in trouble.
If I don’t break my iPod, I won’t get in trouble.
If I break my iPod, I will get in trouble.
If I get in trouble, I will break my iPod.
If I don’t get in trouble, I didn’t break my iPod.
none of the above
4. All of the following statements are true except:
A.
B.
C.
D.
E.
Opposite rays share an endpoint.
The intersection of two planes is a point.
Four non-coplanar points determine space.
Obtuse angles measure more than 90 degrees.
Congruent segments have the same length.
For questions 5-8 translate each of the following into a mathematical expression.
5. The difference of four times a number and 6. Three times the difference of a number and two.
seven.
7. The sum of two and the quotient of a
number and five.
8. The product of four times a number and nine.
HW Set #2 (Problems 9-15)
For #9-12, choose the best answer for each multiple choice question.
9. If A and B are supplementary angles,
what angle relationship between A and B
CANNOT be true?
(A) A and B are right angles
(B) A and B are adjacent angles
(C) A and B are complementary angles
(D) A and B are congruent angles
11. What value of x is a counterexample to the
statement below?
If x 2  8  0 , then x  3 .
(A) 4
(B) 2
(C) -2
(D) -3
10. Which number is a counterexample to the
statement below?
All prime numbers are odd.
(A) 0
(B) 2
(C) 34
(D) 86
12. Which statement is NOT true?
(A) If two lines are parallel, then they lie in one
plane and do not intersect.
(B) Two lines lie in one plane if and only if the
lines are parallel.
(C) If two coplanar lines do not intersect, then the
lines are parallel.
(D) Two lines lie in one plane and do not
intersect if and only if the two lines are parallel.
For questions 13-14, solve each equation. If necessary, leave your answers as reduced fractions.
13.
2
1 5
x  x6
3
2 2
14.
6 3
2
1
 x  x
5 2
5
2
For questions 15-16 translate each of the following into a mathematical expression.
15. Seven less than twice a number
16. Eight more than the quotient of seven and x.
HW Set #3: Problems #16-22
For #16-22, choose the best answer for each multiple choice question.
16. The following statement is an example
17. The following statement is an example of which
of which property:
property?
-11xy + 2x2 = – 11xy + 2x2
2
If  x  4   7 , then 2  x  4  21 .
3
A. Transitive Property of Equality
A. Addition Property of Equality
B. Symmetric Property of Equality
B. Subtraction Property of Equality
C. Reflexive Property of Equality
C. Multiplication Property of Equality
D. Substitution Property of Equality
D. Division Property of Equality
E. Distributive Property of Equality
E. Distributive Property of Equality
Choose the best answer for each multiple choice question. For #18-22, you are completing a
proof.
Given: 5(2x – 6) = 4x + 6
Prove: x = 6
Statements:
1.) 5(2x – 6) = 4x + 6
2.) 10x – 30 = 4x + 6
3.) ______#20_______
4.) 6x = 36
5.) x = 6
Reasons
1.) ______#18_______
2.) ______#19_______
3.) Subtraction Property of Equality
4.) ______#21_______
5.) ______#22_______
18. What reason should be written in the
space marked #18 of this proof?
A. Given
B. Subtraction Property of Equality
C. Distributive Property of Equality
D. Addition Property of Equality
E. Reflexive Property
19. What reason should be written in the space
marked #19 of this proof?
A. Substitution Property of Equality
B. Subtraction Property of Equality
C. Distributive Property of Equality
D. Addition Property of Equality
E. Reflexive Property
20. What statement should be written in the
space marked #20 of this proof?
A. 10x = 4x + 36
B. 6x = 36
C. 6x – 30 = 6
D. None of these
21. What reason should be written in the space
marked #21 of this proof?
A. Substitution Property of Equality
B. Subtraction Property of Equality
C. Distributive Property of Equality
D. Addition Property of Equality
E. Reflexive Property
22. What reason should be written in the
space marked #22 of this proof?
A.
B.
C.
D.
E.
Subtraction Property of Equality
Division Property of Equality
Prove
Addition Property of Equality
Multiplication Property of Equality
HW Set #4: Problems #23-28
For #23-26, choose the best answer for each multiple choice question.
Choose the best answer for each multiple choice question. For #23-26, you are completing a
proof.
Given: AB = XY, BC = YZ
Prove: AC = XZ
Statements
1.) AB = XY
BC = YZ
2.) AB + BC = XY + YZ
3.) AC = AB + BC
XZ = XY + YZ
4.) _____#25_______
Reasons
1.) Given
23. What reason should be written in the space
marked #23 of this proof?
24. What reason should be written in the space marked
#24 of this proof?
A.
B.
C.
D.
E.
A.
B.
C.
D.
E.
Substitution Property of Equality
Subtraction Property of Equality
Segment Addition Postulate
Addition Property of Equality
Definition of Midpoint
2.) _____#23_______
3.) _____#24_______
4.) _____#26_______
Addition Property of Equality
Subtraction Property of Equality
Segment Addition Postulate
Definition of Midpoint
Transitive Property of Equality
25. What statement should be written in the
space marked #25 of this proof?
26. What reason should be written in the space marked
#26 of this proof?
A. AB = XY, BC = YZ
B. AC = XZ
C. AC + XZ = AB + XY + BC + YZ
D. B is the midpoint of AC
A.
B.
C.
D.
E.
E. Y is the midpoint of XZ
Prove
Addition Property of Equality
Subtraction Property of Equality
Substitution Property of Equality
Segment Addition Postulate
For questions 27-28, fill in the reasons for each of the given statements.
27. Given: RT = SU and the figure at the
right.
Prove: RS = TU
Statements:
1.) RT = SU
2.) ST = ST
3.) RT – ST = SU – ST
4.) RT – ST = RS
5.) SU – ST = TU
6.) RS = TU
28. Given: M is the midpoint of AB
Prove: 2  AM  AB
Statements:
1.) M is the midpoint of AB
2.) AM  MB
3.) AM = MB
4.) AM + MB = AB
5.) AM + AM = AB
6.) 2  AM  AB
Reasons:
1.)
2.)
3.)
4.)
5.)
6.)
Reasons:
1.)
2.)
3.)
4.)
5.)
6.)
HW#5: Problems #29-34
For questions 29-32, complete the two column proof for each situation.
29. Given: M is the midpoint of AB
N is the midpoint of CD
AB = CD
Prove: AM = CN
Statements:
1.)
2.)
3.)
4.)
5.) AM + AM = CN + CN
6.) 2AM = 2CN
7.)
30. Given: QS is an angle bisector of
PQR
Prove: m PQS 
Reasons:
1.)
2.) Def. of midpoint
3.) SAP
4.) Substitution prop. of equality
5.)
6.)
7).
1
m PQR
2
Statements:
1.)
2.) m PQS  m SQR
3.) m PQS  m SQR  m PQR
4.) m PQS  m PQS  m PQR
5.) 2m PQS  m PQR
1
6.) m PQS  m PQR
2
Reasons:
1.)
2.)
3.)
4.)
5.)
6.)
31. Given: RT = 5, RS = 5, RT  TS
Prove: RS  TS
Statements:
1.)
2.) RT = RS
3.)
4.)
MORE ON THE NEXT PAGE!!
Reasons:
1.)
2.)
3.) Def. of congruent segments
4.)
32. Given:
Prove:
1 and 2 are complements
1 and 3 are complements
2 3
Statements:
1.)
2.)
Reasons:
1.)
2.) Def. of complementary angles
3.) m 1  m 2  m 1  m 3
4.) m 1  m 1
5.)
6.)
3.)
4.)
5.) Subtraction prop. of equality
6.)
For questions 33-34, set up an equation & solve to find the unknown angle measurement.
33. The sum of an angle, its complement,
and its supplement is 200˚. Find the angle
34. The sum of an angle, its complement, and four
times its supplement is 690˚.
HW#6: Problems #35-49
For questions 35-38, simplify each expression as much as possible. If necessary, leave your
answers as reduced fractions.
5 2
35. 4  3
8 11
37.
4 2

7 3
7 1
36.  
9 6
2
6
38. 8  3
9
7
For questions 39-40, find the midpoint of the segment with the given endpoints.
39. (-8, 9) and (-2, -6)
40. (7, -5) and (-9, -13)
For questions 41-44, solve each equation. If necessary, leave your answers as reduced fractions.
41. 12  5(3r  2)  (r  1)
43.
4
7
5
1
x   x
3
6
9
3
42.
10  7 y 5  y

4
3
44.
3
4 1
 3x     6 x  7 
4
6 2
45. Find the missing endpoint of HG if H has coordinates (5, -2) and the midpoint of HG is (-4, 8).
For questions 46-49, find the value of the variable(s).
46.
47.
(7x+37) 
3y
4x
(5x-10)
(4x+4)
(5y-80) 
48.
m LMN  140
49.
P
L
(11x-9) 
(2x+2)
(5x+5)
M
N
(x+1) 